eigen
Very LowFormal, Technical, Academic
Definition
Meaning
A term from mathematics, especially linear algebra, meaning a property or value that is intrinsic, characteristic, or invariant under a given transformation, often specifically referring to eigenvalues or eigenvectors.
While strictly a technical term, it can be used metaphorically in scientific or data-focused contexts to describe an intrinsic, essential, or defining characteristic of a system or entity. It is not used in everyday English.
Linguistics
Semantic Notes
"Eigen" is almost exclusively used as part of compound nouns in English, primarily 'eigenvalue' and 'eigenvector'. It is a direct loan from German and is not an independent English word in common parlance. Its use indicates a highly technical, mathematical context.
Dialectal Variation
British vs American Usage
Differences
No significant differences in meaning or usage between British and American English, as it is a precise technical term. Spelling conventions for related terms (e.g., 'behaviour' vs. 'behavior') do not affect this term.
Connotations
Purely technical and neutral. No emotional or cultural connotations.
Frequency
Identically rare in both dialects, confined to specialised fields.
Vocabulary
Collocations
Grammar
Valency Patterns
Used as a bound morpheme preceding a noun (e.g., eigenvector).Vocabulary
Synonyms
Strong
Neutral
Weak
Vocabulary
Antonyms
Phrases
Idioms & Phrases
- “None in common English usage.”
Usage
Context Usage
Business
Virtually unused, except perhaps in highly quantitative finance or data science roles when discussing principal component analysis.
Academic
Core terminology in mathematics, physics (especially quantum mechanics), engineering, computer science, and data science.
Everyday
Not used.
Technical
Fundamental term in linear algebra, quantum physics, vibration analysis, and machine learning.
Examples
By Part of Speech
verb
British English
- Not applicable.
American English
- Not applicable.
adverb
British English
- Not applicable.
American English
- Not applicable.
adjective
British English
- Used attributively: The eigen decomposition reveals the system's structure.
American English
- Used attributively: The eigen values were calculated using iterative methods.
Examples
By CEFR Level
- (Not applicable for this level.)
- (Not applicable for this level.)
- Scientists calculated the eigenvalues to understand the material's resonant frequencies.
- In data science, principal components are the eigenvectors of the covariance matrix.
- The stability of the system hinges on the dominant eigenvalue of the state transition matrix.
- She derived the eigenfunctions of the Hamiltonian operator to solve the quantum mechanical problem.
Learning
Memory Aids
Mnemonic
Think: 'EYE-gen' values are the 'I' (self) values of a matrix – they reveal its intrinsic character.
Conceptual Metaphor
THE ESSENCE IS AN EIGENVALUE (e.g., "Finding the eigenvector of the problem helped us identify its core component.")
Watch out
Common Pitfalls
Translation Traps (for Russian speakers)
- Do not confuse with 'eigen' meaning 'own' in German. In Russian, equivalents are 'собственный' (собственное значение, собственный вектор), which directly mirrors the German 'Eigenwert'.
- The English pronunciation /ˈaɪɡən/ is non-intuitive; avoid a hard 'g' as in 'get'.
Common Mistakes
- Using 'eigen' as a standalone adjective in non-technical writing (e.g., 'That is an eigen property' is incorrect).
- Mispronouncing it as /ˈiːdʒən/ or /ˈeɪɡən/.
Practice
Quiz
In which field is the term 'eigen' most commonly used?
FAQ
Frequently Asked Questions
No, it is almost never used alone. It is a combining form used in technical compounds like eigenvalue.
It means 'own' or 'peculiar to' (e.g., 'Eigenheim' means 'own home'). The mathematical sense derives from 'characteristic to itself'.
Pronounce it as EYE-gen, rhyming with 'tie' and then 'gen' as in 'generator'.
Rarely. It might appear metaphorically in advanced discussions of systems theory, complex data analysis, or philosophy of science, but its use remains highly specialised.